Difference schemes for nonlocal reverse parabolic problem with second kind boundary and integral conditions

In this work, second kind boundary and integral conditions for reverse parabolic differential equations and nonlocal problem are studied. In order to find the approximate solution of the nonlocal problem, first and second order finite difference schemes are constructed. The stability of the first and second order finite difference schemes for the Neumann type boundary value problem with integral conditions are proved In addition, the difference schemes with the first and second order accuracy for the multidimensional reverse parabolic partial differential equation given by Neumann conditions are discussed. MATLAB codes to find numerical solution of the integral type nonlocal reverse parabolic boundary value problem with Neumann condition in test examples are given.